Is the hamza pronounced in words where it is not written, such as "المؤمنون" (al-Mu'minūn) and "بيس" (bi's), and is the alif in "المنفوش" (al-Manfūsh) pronounced as the questioner hears it from the reciter?

The Mus'haf you are reading from is written according to the recitation of Warsh from Nafi', which is the prevalent recitation in Morocco. Warsh, and those who agree with him, replace the hamza with an extension of the letter preceding it. As for the word "al-manfūsh" (المنفوش) in Surat al-Qāri'ah, there is consensus among all mutawatir reciters regarding it. It is recommended to learn the Quran orally from a skilled shaykh, and to assist oneself by listening to recitations of the reciters, rather than relying solely on reading from the Mus'haf or depending entirely on listening to recitations via media, due to the possibility of error and the inability to master listening.